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Linear bound for the dyadic paraproduct on weighted Lebesgue space
The dyadic paraproduct is bounded in weighted Lebesgue spaces if and
only if the weight belongs to the Muckenhoupt class . However, the
sharp bounds on the norm of the dyadic paraproduct are not known even in the
simplest case. In this paper we prove the linear bound on the norm of
the dyadic paraproduct in the weighted Lebesgue space using Bellman
function techniques and extrapolate this result to the case.Comment: 13 page
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